function Invoke-MyCmdlet {
    [CmdletBinding(SupportsShouldProcess = $true)]
    param()
    # ...
}

if ($PSCmdlet.ShouldProcess("Target of action")) {
    # Do the thing
}

When using -WhatIf:

What if: Performing the action "Invoke-MyCmdlet" on target "Target of action"

When using -Confirm:

Are you sure you want to perform this action?
Performing operation "Invoke-MyCmdlet" on target "Target of action"
[Y] Yes  [A] Yes to All  [N] No  [L] No to All  [S] Suspend  [?] Help (default is "Y"):

Other examples couldn't clearly explain to me how to trigger the conditional logic.

This example also shows that underlying commands will also listen to the -Confirm flag!

<#
Restart-Win32Computer
#>

function Restart-Win32Computer 
{
    [CmdletBinding(SupportsShouldProcess=$true,ConfirmImpact="High")]
    param (
    [parameter(Mandatory=$true,ValueFromPipeline=$true,ValueFromPipelineByPropertyName=$true)]
    [string[]]$computerName,
    [parameter(Mandatory=$true)]
    [string][ValidateSet("Restart","LogOff","Shutdown","PowerOff")] $action,
    [boolean]$force = $false
)
BEGIN {
# translate action to numeric value required by the method
switch($action) {
    "Restart"
    {
        $_action = 2
        break
    }
    "LogOff"
    {
        $_action = 0
        break
    }
    "Shutdown"
    {
        $_action = 2
        break
    }
    "PowerOff"
    {
        $_action = 8
        break
    }
}
# to force, add 4 to the value
if($force) 
{
    $_action += 4
}
write-verbose "Action set to $action"
}
PROCESS {
    write-verbose "Attempting to connect to $computername"
    # this is how we support -whatif and -confirm
    # which are enabled by the SupportsShouldProcess
    # parameter in the cmdlet bindnig
    if($pscmdlet.ShouldProcess($computername)) {
        get-wmiobject win32_operatingsystem -computername $computername | invoke-wmimethod -name Win32Shutdown -argumentlist $_action
    }
}
} 
#Usage:
#This will only output a description of the actions that this command would execute if -WhatIf is removed.
'localhost','server1'| Restart-Win32Computer -action LogOff -whatif 

#This will request the permission of the caller to continue with this item.
#Attention: in this example you will get two confirmation request because all cmdlets called by this cmdlet that also support ShouldProcess, will ask for their own confirmations...
'localhost','server1'| Restart-Win32Computer -action LogOff -Confirm